Bernoulli Meets PBFT: Modeling BFT Protocols in the Presence of Dynamic Failures

Abstract

The publication of the pivotal state machine replication protocol PBFT laid the foundation for a large body of BFT protocols. While many successors to PBFT have been developed, there is no general technique to compare these protocols under realistic network conditions such as unreliable links. In this paper, we introduce a probabilistic model for evaluating BFT protocols in the presence of dynamic link and crash failures. Based on modeling techniques from communication theory, the network state of replicas is captured and used to derive the success probability of the protocol execution. To this end, we examine the influence of link and crash failure rates as well as the number of replicas. The model is derived from the communication pattern, making it implementation-independent and facilitating an adaptation to other BFT protocols. The model is validated with a simulation of PBFT and BFT-SMaRt. Further, a comparison in protocol behavior of PBFT, Zyzzyva and SBFT is performed and critical failure thresholds are identified.